MPs across the political divide should “abandon outrage” and attempt to “forge a consensus” over Brexit, Work and Pensions Secretary Amber Rudd has said.
In the Daily Mail, Ms Rudd wrote: “Brexit is in danger of getting stuck.”
It comes after the PM’s bid to make her Brexit deal more acceptable to MPs suffered a blow when EU leaders said it was “not open for renegotiation”.
Meanwhile, ex-UKIP leader Nigel Farage has told the BBC that he thinks there might be another referendum.
Labour has said the withdrawal deal is now “dead in the water”.
Theresa May travelled to Brussels earlier this week to make a special plea to EU leaders after delaying Tuesday’s Commons vote on the deal, in anticipation of a heavy defeat.
She then went on to win a confidence vote brought by her own MPs but vowed to listen to the concerns of the 37% of Tory MPs who voted against her.
Many of her own MPs are concerned that the controversial “backstop” plan – which is aimed at preventing a hard border in Northern Ireland – would keep the UK tied to EU rules indefinitely and limit its ability to strike trade deals.
Ms Rudd – who supported Remain in the referendum – said she supported Mrs May’s deal and advocated assembling a “coalition” to avoid what she called “the rocks of no deal”.
She said the country “will face serious trouble” if MPs “dig in against the prime minister’s deal”.
“We need to find a plan that a majority in Parliament can support,” she said.
“We need to try something different. Something that people do in the real world all the time, but which seems so alien in our political culture – to engage with others and be willing to forge a consensus.
“It also requires everyone to abandon outrage and accusations.”
Ms Rudd said she believed the UK could have “a fantastic post-Brexit future”, but only if politicians “try a different way”.
One idea, favoured by at least one other cabinet minister, is a series of votes on other plans, such as a relationship similar to Norway’s with the EU, or another referendum, before next month’s “meaningful vote” in the Commons.
At a Leave Means Leave rally in London on Friday, Mr Farage told the BBC it was “outrageous” another referendum could happen, but added: “I can see where we’re going.”
Mr Farage added the treatment of Mrs May in Brussels this week had been a “shaming moment” for both the UK and the EU and that the PM’s Brexit deal was now “dead”.
After Mrs May addressed EU leaders at the summit on Thursday evening, European Commission President Jean-Claude Juncker urged further clarity from the UK.
He said: “Our UK friends need to say what they want, instead of asking us to say what we want… because this debate is sometimes nebulous and imprecise.”
Video footage of the two on Friday morning captured a tense exchange, apparently about his remarks, although the exact words were not audible.
Asked about what she had said to him, Mrs May told reporters they had had a “robust discussion”.
“And what came out of that was his clarity that actually he’d been talking – when he used that particular phrase – he’d been talking about a general level of debate,” she said.
At a later press conference, Mr Juncker described Mrs May as a “good friend” who he admired as a “woman of courage”.
He said he had not realised nebulous was a word in English and he had been referring, not to her, but to the “overall state of the debate in Britain”.
Labour leader Jeremy Corbyn said: “The last 24 hours have confirmed that Theresa May’s Brexit deal is dead in the water. The prime minister has utterly failed in her attempts to deliver any meaningful changes to her botched deal.
“Rather than ploughing ahead and dangerously running down the clock, the prime minister needs to put her deal to a vote next week so Parliament can take back control.”